First slide

Instantaneous acceleration

Question

Velocity (v) versus displacement (x) plot of a body moving along a straight line is as shown in the graph. The corresponding plot of acceleration (a) as a function of displacement (x) is

Moderate

A
B

c
C
D

Solution

Acceleration
$\large a = \frac{{dv}} {{dt}} = v\frac{{dv}} {{dx}}$

Now for 0 ≤ x ≤ 100, v = kx
dv/dx = k
a = k(kx) = k²x
Again for 100 ≤ x ≤ 200, dv/dx = -k and v = c - kx
a = (-k)(c - kx) = k²x - kc.
Therefore option (4) is correct.

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